Henry's constants will be estimated by using of Krichevsky-Kazarnovsky and Krichevsky-Ilinskaya .... ESTIMATION OF HENRY'S CONSTANTS. 281. RT. V. P.
ESTIMATION OF HENRY’S CONSTANTS FROM HIGH PRESSURE GAS SOLUBILITIES. THE SYSTEMS CO2 + nHEXANE AND N2O + n-HEXANE I.Găinar*, Daniela Bala abstract: Experimental determination of gas solubilities of CO2 and N2O in n-hexane (at pressures up to 50 bar and temperatures 0, 5, 10, 15 and 250C) will be presented. Henry’s constants will be estimated by using of Krichevsky-Kazarnovsky and Krichevsky-Ilinskaya equations.
Introduction The solubility of gases in liquids is an area of active interest from both the theoretical and practical standpoints. Both the dilute solutions resulting from the low solubility of many gases in liquids, and the large variety of sizes, shapes and polarities of gas molecules to act as “probes” have made the solubility of gases in liquids an excellent tool to investigate the test theories of liquid properties and liquid structure. A knowledge of the solubility of gases is of practical importance in various industrial processes, in the study of artificial atmospheres for divers and astronauts, in the interaction of gases with our environment, in processes for saline water demineralization, and in the study of various biological fluids and tissues [1]. This paper deals with experimental determination of gas solubilities of CO2 and N2O in nhexane (at pressures up to 50 bar and temperatures 0, 5, 10, 15 and 250C) and from these values we have calculate the Henry’s constants by using of Krichevsky-Kazarnovsky and Krichevsky-Ilinskaya equations.
Theoretical considerations From theoretical point of view, problem of gas solubility in liquids represents a particular case of liquid – vapor phase equilibrium.
* *Department of Physical Chemistry, Faculty of Chemistry, University of Bucharest, 4-12 Bd. Regina Elisabeta,70346 Bucharest, Romania
Analele UniversităŃii din Bucureşti – Chimie, Anul XIV (serie nouă), vol. I-II, pg. 279-285 Copyright © 2005 Analele UniversităŃii din Bucureşti
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(C1 + C 2 )l
⇔ C 2g
(1)
The general relation which governs this process derive from general condition of thermodynamic equilibrium, namely:
µ 2l = µ 2g , or f 2l = f 2g
(2)
By introduction of significance of solute fugacity in both phases we obtain:
f 20,l ⋅ γ 2l ⋅ x2l = x2g ⋅ γ 2g ⋅ P
(3)
that represents generalised form of Raoult’s law. Because Henry’s law shows the proportionality between gas fugacity and its concentration in the solution,
f 2g = H ⋅ x 2l
(4)
results that the product f 20,l ⋅ γ 2l represent just the Henry’s constant (which depends on the nature of both components – depends on the nature of solvent by means of activity coefficient γ 2l ). The Henry’s constant depends only on the temperature. Taking as standard state the ideal dilute solution, even by definition of Henry’s constant, it means that for a concentrate solution (at high pressures) the equation (4) should be corrected by introduction of the activity coefficient in asymmetric convention, γ 2*,l :
γ 1l → 1 γ
*,l 2
→1
when when
x1l → 1 x →0 l 2
for solvent and for solute
Introduction of asymmetric convention of normalization eliminates the arbitrary in the definition of f 20,l (standard state fugacity of solute), which can be experimentally determinate: s fg f 20,l = lim 2l = H 2P,11 x2l →0 x 2
where
(5)
Ps
H 2,11 represents the Henry’s constant for solute 2 in solvent 1 at the system
temperature and the P1s (the saturation pressure of pure solvent). As long as the pressure is not large, the pressure dependence of Henry’s constant can be neglected. At high pressure the effect is not negligible and therefore it is necessary to consider how Henry’s constant depends on pressure. This dependence is obtain by using the equation:
ESTIMATION OF HENRY’S CONSTANTS
∂ ln f 2l ∂P
281
l
V2 = l T , x2 RT
(6)
l
where V 2 is the partial molar volume of solute in the liquid phase. By substitution of relation (5) in equation (6) we finally obtain:
(
∞ ,l
fg V 2 ⋅ P − P1s Ps ln 2l = ln H 2,11 + RT x2
)
(7) ∞ ,l
where we assume that the partial molar volume at infinite dilution, V 2 , is independent on pressure. The above equation is known as Krichevsky-Kasarnovsky equation. This equation is very useful for representing solubilities of sparingly soluble gases to very high pressures. In more cases is not reasonable to expect that the activity coefficient of the solute in the liquid phase is independent of composition or that the partial molar volume is constant. Variation of the activity coefficient of the solute with the mole fraction can be given by two-suffix Margules equation:
ln γ 1l =
( )
A ⋅ x 2l RT
2
(8)
where A is an empirical constant determined by intermolecular forces in the solution. The activity coefficient γ 2*,l of the solute normalized according to the unsymmetric convention is found from the Gibbs-Duhem equation:
ln γ 2*,l =
[(
A ⋅ x1l RT
)
2
]
−1
(9)
The fugacity of component 2 at pressure P1s is: Ps
f 2l = γ 2*,l ⋅ H 2,11 ⋅ x 2l
(10)
Instead of equation (7) we obtain:
[(
fg A Ps ln 2l = ln H 2,11 + ⋅ x1l RT x2
)
2
]
∞ ,l
(
V 2 ⋅ P − P1s −1 + RT
)
(11)
Equation (11) is known as Krichevsky-Ilinskaya equation. For liquid-gas solutions, Krichevsky-Ilinskaya equation represents a significant improvement with regard of Krichevsky-Kasarnovsky equation. Between the three parameters of the equation, the Henry’s constant is the most important. Henry’s constant ∞ ,l
has always positive values while A and V 2
can be positive or negative [2-9].
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Materials and method Principle of experimental method as well as working procedure and analysis of obtained data were presented in a previous work [10]. N-hexane was a Merck Schuchardt solvent zur Synthese (d at 200C is 0.659), carbon dioxide was a pure Linde gas (99.9%) and N2O was for medical use. Experimental parameters were measured with high precision (working pressure ± 0.01 bar, working temperature ± 0.020C, pressure of desorbed gas ± 0.05 mm Hg, and mass of solvent- with analytical balance).
Results and Discussions Tables 1 and 2 contain the Henry’s constants calculated from both methods (KrichevskyKazarnovsky and Krichevsky-Ilinskaya equations). These data were obtained by using of experimental solubilities values of CO2 and N2O in n-hexane at various temperatures and pressures [11]. The gas fugacities at different temperatures and pressures were calculated by using of computing programme based on Redlich-Kwong equation:
ln f = ln where a = 0.42748 ⋅ R 2 ⋅
RT a V b a + ln + − 3/ 2 3/ 2 V − b bRT V + b V − b RT (V + b )
Tc2 T and b = 0.08664 ⋅ R ⋅ c . Pc Pc
For CO2: Tc = 304.1 K and Pc = 73.8 atm. For N2O: Tc = 309.6 K and Pc = 72.4 atm. Because experimental measurements were performed at high pressures, the vapor pressure of pure solvent, P1s , can be neglected. Table 1 Calculated data for the system CO2 + n-hexane
T [K]
273.15
P [bar]
37.43 36.26 32.04 30.38 24.85 20.58 12.74 5.68
x
l 2
0.450 0.380 0.365 0.331 0.219 0.204 0.122 0.058
f
g 2
28.78 28.15 25.72 24.69 18.90 17.96 11.73 5.48
ln
f 2g x2l
4.16 4.31 4.26 4.31 4.46 4.48 4.56 4.55
f 2g
∞
(
V2 ln l − ⋅ P − P1s x 2 RT 4.07 4.22 4.18 4.24 4.40 4.27 4.53 4.54
H 2,1
) K-K (eq. 7)
K-I (eq. 11)
108.10
105.15
ESTIMATION OF HENRY’S CONSTANTS
278.15
283.15
288.15
298.15
44.00 39.00 29.10 21.46 8.13 41.45 41.25 30.96 21.75 12.54 44.78 41.25 33.51 30.87 21.75 9.99 52.33 41.65 41.35 31.85 31.65 26.75 15.68 11.85 7.05
0.508 0.421 0.281 0.194 0.071 0.379 0.368 0.260 0.176 0.094 0.351 0.340 0.254 0.222 0.152 0.073 0.350 0.265 0.261 0.203 0.201 0.169 0.100 0.081 0.046
32.63 30.11 24.15 18.76 7.74 31.92 31.82 25.64 19.12 11.66 34.23 32.30 27.59 25.85 19.24 9.46 39.33 33.40 33.22 27.01 26.87 23.32 14.49 11.17 6.81
4.16 4.27 4.45 4.57 4.69 4.43 4.46 4.59 4.69 4.82 4.58 4.55 4.69 4.76 4.84 4.86 4.72 4.84 4.85 4.89 4.90 4.93 4.98 4.93 4.99
283
4.06 4.17 4.38 4.52 4.67 4.33 4.36 4.52 4.64 4.79 4.47 4.46 4.61 4.69 4.79 4.84 4.60 4.74 4.75 4.82 4.83 4.87 4.94 4.90 4.98
127.89
126.43
144.98
144.34
149.04
150.14
158.35
160.77
Table 2 Calculated data for the system N2O + n-hexane
T [K]
273.15
278.15
283.15
288.15
P [bar]
29.60 24.79 19.70 15.20 9.70 6.08 30.90 24.60 19.11 14.80 10.09 5.78 30.38 24.89 20.09 14.99 10.19 5.68 31.75 26.56 21.85 16.46 10.39
x
l 2
0.486 0.351 0.275 0.212 0.154 0.084 0.393 0.309 0.235 0.184 0.131 0.092 0.351 0.292 0.229 0.167 0.116 0.085 0.311 0.259 0.221 0.176 0.117
f
g 2
24.20 21.00 17.30 13.77 9.12 5.85 25.32 21.06 16.97 13.51 9.49 5.58 25.26 21.45 17.84 13.73 9.61 5.50 26.44 22.83 19.32 15.02 9.80
fg ln 2l x2 3.91 4.09 4.14 4.17 4.14 4.24 4.17 4.22 4.28 4.29 4.28 4.11 4.28 4.30 4.36 4.41 4.42 4.17 4.44 4.48 4.47 4.45 4.43
f 2g
∞
(
V2 ln l − ⋅ P − P1s x 2 RT 3.84 4.03 4.09 4.13 4.12 4.23 4.09 4.16 4.23 4.26 4.26 4.09 4.20 4.24 4.31 4.37 4.39 4.16 4.37 4.42 4.42 4.41 4.40
H 2,1
) K-K (eq. 7)
K-I (eq. 11)
74.40
76.05
84.54
81.28
90.76
92.68
96.54
98.00
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I. GĂINAR et al. 34.50 29.98 25.48 19.89 14.50 8.03
298.15
0.287 0.258 0.219 0.168 0.133 0.072
4.61 4.60 4.63 4.67 4.62 4.68
28.82 25.68 22.37 17.98 13.48 7.72
4.53 4.54 4.57 4.63 4.59 4.66
108.34
110.15
For system CO2 + n-hexane at 250C, in the case when we have obtained the Henry’s fg constants by using of Krichevsky-Kazarnovsky equation, we represented ln 2l versus x2 pressure (figure 1), and when we used Krichevsky-Ilinskaya equation, we represented ∞
f 2g
(
[
)
( )]
ln [f2g/x2l]-V2(P-P1s)/RT
2 V2 ln l − ⋅ P − P1s versus 1 − x1l (figure 2). In both cases we obtained a straight line x 2 RT that allow a good extrapolation of Henry’s constants.
ln [f2g/x2l]
5.1 5 4.9 4.8 4.7 0
10
20
30
40
50
5.1 5 4.9 4.8 4.7 4.6 4.5 0
60
0.2
0.4
0.6
1-(x1l)2
P [bar]
Fig. 1. Solubility of CO2 in n-hexane at high pressures at 250C (Krichevsky-Kazarnovsky equation)
Fig. 2. Solubility of CO2 in n-hexane versus molar fractions at 250C (Krichevsky-Ilinskaya equation) Ps
In figures 3 and 4 we represented the Henry’s constants, H 21,1 (obtained from KrichevskyKazarnovsky and Krichevsky-Ilinskaya equations) versus temperature for both systems. 200
200 150
CO2 100
N2O
50
CO2 100
N2O
50
0 270
H2,1
H2,1
150
0 280
290
300
T [K]
Fig. 3. Temperature dependence of Henry’s constants for CO2 and N2O in n-hexane calculated with Krichevsky-Kazarnovsky equation
270
280
290
300
T [K]
Fig. 4. Temperature dependence of Henry’s constants for CO2 and N2O in n-hexane calculated with Krichevsky-Ilinskaya equation
ESTIMATION OF HENRY’S CONSTANTS
285
We remark an excellent agreement between the values of Henry’s constants calculated with the equation (7) and (11).
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Krichevsky, I. R. and Kasarnovsky, J. S. (1935) J. Am. Chem. Soc., 57, 2168
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